本研究探討了將階層阿基米德耦合（HAC, Hierarchical Archimedean Copula）模型與網絡分析方法結合，應用於投資組合優化的效果。研究首先通過de-GARCH 技術對財務時間序列進行預處理，以消除數據中的自相關性（Autocorrelation）、條件異方差（Conditional Heteroskedasticity）與波動聚集效應（Volatility Clustering）。接 著，我們計算de-GARCH 處理後的多變量序列之相似性矩陣（Similarity Matrix），並構建全域最小生成樹（MST, Minimum Spanning Tree），以篩選出適合投資組合的股票標的。接下來，我們採用HAC 模型以建構所選股票之聯合分佈結構。之後，基於這種聯結網絡（Connected Network）的聯合分佈，我們確定投資組合中各個股票的最優權重（Optimal Weights）。實證研究使用了S&P100 指數中2019 年至2022年的成分股數據，並採用移動視窗（Rolling Window）方法進行測試。數值結果顯 示，與傳統方法相比，所提出的模型能夠在投資組合優化中取得顯著的累積報酬（Cumulative Return），展示了本方法在風險管理（Risk Management）與收益最大化（Return Maximization）上的潛在優勢。;This study explores the integration of Hierarchical Archimedean Copula (HAC) models with network analysis methods for portfolio optimization. We first employ de-GARCH techniques to preprocess financial time series data, eliminating inherent characteristics such as autocorrelation, conditional heteroskedasticity (ARCH/GARCH), and volatility clustering. Subsequently, we compute the similarity matrix of the multivariate de-GARCH sequences and construct a global Minimum Spanning Tree (MST) to identify stocks suitable for portfolio selection. Next, we use the HAC model to capture the joint distribution of the selected stocks. The joint distribution based on the connected network is utilized to determine the optimal weights of the selected stocks within the portfolio. The empirical study is conducted using S&P100 index constituent stocks from 2019 to 2022, adopting a rolling window approach for validation. Numerical results indicate that the proposed method achieves satisfactory cumulative returns, demonstrating its potential advantages in risk management and return maximization, outperforming traditional methods.
